The german lands east of the river Elbe have been different from the western parts of Germany for more than a 1000 years. In the historical record you see a pretty sharp change in marriage patterns,land ownership and political structure when crossing the Elbe.

The enlightenment was less influential in the rural estates of the ultra conservative east elbian Junkernklasse than it was in the more densely populated Rhineland regions. Fukuyama has a nice chapter on the matter in “The Origins of Political Order”.

On top of that you have the separation, and the dislike of the GDR to foster critical thinking and the economic collapse of the east after reunification that lead to a lot of brain drain.

Disenfranchisement, after reunification they were left with little generational wealth, liberalism spiraled them deeper into a hopeless situation, no jobs, no economic future, impoverishment. Under liberalism the only alternative offered to them is the far right.

During the cold war and after, the US and anglosphere was mostly interested in the destruction of left ideology, labor unions, left parties etc. were all targeted. The right offers a safe outlet for people with those grievances, it doesn't threaten capital, so it was always allowed to linger in Germany not just in the east. It's deeply rooted in establishment and civil organizations, in university fraternities (schlagende verbindungen, the CSU etc.). The allied supported and used and bolstered far right groups all around Europe (Gladio, NSU, etc.) in their fight against socialism and people on the left. We still feel the effects to this day and state and federal police and intelligence still operate this way.

Protests in Germany you see police protecting far right groups from leftists, not the other way around. It's a necessary aspect of liberalism to allow the disenfranchised the outlet into right wing extremism.